The MBTI dichotomies, which substantially line up with four of the Big Five dimensions, now have decades of studies in support of their validity and reliability, while the "cognitive functions" — which James Reynierse (in the 2009 article linked below) refers to as a "category mistake" — have barely been studied. And the reason they've barely been studied is that, unlike the dichotomies, they've never been taken seriously by any significant number of academic psychologists. Going all the way back to 1985, the MBTI Manual described or referred to somewhere in the neighborhood of 1,500 MBTI studies and, as I understand it, not one
of the many study-based correlations reported in the manual were framed in terms of the functions. And many more dichotomy-based studies have been done in the years since. The third edition of the MBTI Manual was published in 1998 and, as Reynierse notes in the linked article, it cited a grand total of eight studies
involving "type dynamics" (i.e., the functions model) — which Reynierse summarizes as "six studies that failed, one with a questionable interpretation, and one where contradictory evidence was offered as support."
Dario Nardi's one of the leading cognitive functions guys (as I'm sure you know), and his test
is arguably the most-linked-to cognitive functions test — but, as further discussed in this INTJforum post,
INTJs typically get high Ni scores and high Ne scores
(with Ni not substantially favored over Ne), and high Te scores and high Ti scores
(with Te not substantially favored over Ti), when they take Nardi's test.
As I understand it, there isn't a single function-based test on or off the internet on which INTJs reliably get high Ni and Te scores and low Ti and Ne scores and INTPs reliably get high Ti and Ne scores and low Ni and Te scores — never mind scoring the third and fourth functions in a way that matches the model.